Nonlinear Dissipation in Two-Dimensional Helium Films.

Nonlinear superflow dissipation in very thin ((TURN)1 atomic layer) films was studied using the technique of third sound resonance, in which a superfluid wave motion analogous to shallow water waves is induced on the inner surface of a cavity. The superfluid velocity on resonance is linear in drive strength at low velocities, but at higher powers the superflow enters a nonlinear regime where the velocity saturates and the resonance Q falls rapidly. A number of recent theories, based on the Kosterlitz-Thouless picture of phase transitions in two-dimensional systems, have explicit predictions for the functional form and parameters of the nonlinear dissipation. A model employing these predictions was developed and solved by ignoring deviations from sinusoidal motion for resonances with sufficiently high Q. A nonlinear dissipation function varying exponentially in the superfluid velocity explains the data better than a power law dissipation. A sharp decline in the exponential limiting velocity scale is observed as the transition temperature is approached, as has been seen in related measurements on thicker films. Superfluid velocities are derived through thermodynamic calculations involving film and cell parameters. These calculated velocities are very large for the lowest temperatures and reasons for this anomaly are discussed. Possible nonlinear frequency shifts due to the substrate potential and to film heating are analyzed. The low temperature (<(, ).5 K) low power Q of third sound resonances has been observed to saturate at about 10('4). At low temperatures in liquid helium, the phonon-phonon scattering rate declines rapidly and it is proposed that this Q saturation is due to a transition from the hydrodynamic ((omega)(tau) << 1) to the collisionless ((omega)(tau) >> 1) regime.